Consistent Approximations to Impulsive Optimal Control Problems

TL;DR

This paper applies the theory of consistent approximations to impulsive optimal control problems, demonstrating convergence of solutions from reparametrized approximations to the original problem.

Contribution

It introduces a reparametrization approach for impulsive control problems and proves convergence of solutions from approximations to the original problem.

Findings

Convergence of approximate solutions to the reparametrized problem.

Method to recover solutions of the original problem from reparametrized solutions.

Validation of the approximation approach for impulsive control systems.

Abstract

We analyse the theory of consistent approximations given by Polak and we use it in an impulsive optimal control problem. We reparametrize the original system and build consistent approximations for this new reparametrized problem. So, we prove that if a sequence of solution of the consistent approximations is converging, it will converge to a solution of the reparametrized problem, and, finally, we show that from a solution of the reparametrized problem we can find a solution of the original one.